Classification of multiplicity free Hamiltonian actions of complex tori on Stein manifolds

Details Classification of multiplicity free Hamiltonian actions of complex tori on Stein manifolds Classification of multiplicity free Hamiltonian actions of complex tori on Stein manifolds

2007-06-05

arxiv.org/abs/0706.0632v2

J. Sympl. Geom. 7(2009), 295-310

Mathematics

Symplectic Geometry

12 pages, v2 minor corrections made

Scientific paper

A Hamiltonian action of a complex torus on a symplectic complex manifold is said to be {\it multiplicity free} if a general orbit is a lagrangian submanifold. To any multiplicity free Hamiltonian action of a complex torus $T\cong (\C^\times)^n$ on a Stein manifold $X$ we assign a certain 5-tuple consisting of a Stein manifold $Y$, an \'{e}tale map $Y\to \t^*$, a set of divisors on $Y$ and elements of $H^2(Y,\Z)^{\oplus n}, H^2(Y,\C)$. We show that $X$ is uniquely determined by this invariants. Furthermore, we describe all 5-tuples arising in this way.

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